Simulating the spread of infection in networks with quantum computers

Many classical stochastic processes can be modeled as Markovian processes, including the spreading of infection in networks. Simulating the Markovian processes using classical computers is generally unscalable for large networks. In this seminar, I will introduce the Hamiltonian evolution on quantum computers and how the Markovian spreading of infection can be efficiently simulated using the Hamiltonian evolution. In particular, we analytically and numerically analyze the evolution of a specifically designed Hamiltonian, and prove that the evolution simulates a classical Markovian process, which describes the well-known epidemiological stochastic susceptible and infectious (SI) model. As an example, we simulate the infection spreading process of the SARS-CoV-2 variant Omicron in a small-world network. The simulation results are qualitative consistent with the infection spreading in the west coast of USA.